Covector transport and the criterion

This is the separation the sheet asked for, stated correctly: the bulk term is all of ${\mathcal{I}}_{\mathrm{sol}}$, and nothing is left over inside the class. What the shell sees is ${\mathsf{W}}_u$. A remainder appears only when $u$ is compared with a candidate $\tilde{u}$ satisfying (eq:mc); by (a), the comparison is decided by ${\mathsf{W}}_u$ alone, and by (b) the candidate exists exactly when (eq:criterion) holds.